A presidential spokesman said he is in a “serious but stable condition”, although he was able to breathe on his own – a “positive sign”.
Mr Mandela, 94, has been ill for some days but deteriorated overnight and was transferred to a hospital in Pretoria.
He led the fight against apartheid and is regarded as the father of democratic South Africa.
He has recently suffered a series of health problems and this is his fifth visit to hospital in two years.
In April he was released from hospital after a 10-day stay caused by pneumonia.
His illness was described on Saturday as a recurrence of a lung infection, which has troubled him repeatedly.
Mr Mandela was taken to hospital, from his home in a suburb of Johannesburg, at about 01:30 local time (23:30 GMT Friday).
Mac Maharaj, South Africa’s presidential spokesman, told the BBC he was receiving expert medical care.
Doctors were doing everything possible to make him comfortable and better, he added.
“What I am told by doctors is that he is breathing on his own and I think that is a positive sign,” he said.
Mr Mandela’s wife Graca Machel had been at his bedside since the early hours of the morning, Sapa news agency quoted the presidential spokesman as saying.
She cancelled a scheduled appearance at a meeting in London.
“Naturally the immediate members of the family have access to him and it’s always good for the patient that he has been accompanied by one or other of them, and that has happened,” Mr Maharaj told the BBC.
‘Symbol of hope’
“President Jacob Zuma, on behalf of government and the nation, wishes Madiba a speedy recovery and requests the media and the public to respect the privacy of Madiba and his family,” Mr Maharaj said in a statement, using the clan name by which Mr Mandela is often known.
On the streets of Pretoria, people expressed their affection for their former president and their concern.
Mamoshomo Tswai, a trader, said: “As long as Tata [father] is still alive then poor people like me, people who are down down, single mothers like me, we still have hope. South Africa is nothing without him.”
But another informal trader in Pretoria, who did not want give their name, said: “We must just accept that he is old. We love him, we all do, but we must start to accept that he is a very old man.”
Keith Khoza, a spokesman for the governing ANC, said Mr Mandela continued to be “a symbol of hope, to be a symbol of reconciliation” for South Africa.
“We are certainly concerned about his health and we called on South Africans to pray for him and his family.
“Even if you have an elderly person in the family who is sick and you expect something – once it happens the shock is still there.”
Mr Mandela served as president from 1994 to 1999.
He was previously imprisoned for 27 years, and is believed to have suffered damaged lungs while working in a prison quarry.
He contracted tuberculosis in the 1980s while being held in jail on the windswept Robben Island.
He retired from public life in 2004 and has been rarely seen in public since.
There was a row in April when South Africa’s governing African National Congress (ANC) – Mr Mandela’s party – filmed a visit to see him and broadcast the pictures of him with President Zuma and other party figures.
Critics called it an invasion of his privacy.
Mr Mandela was awarded the Nobel Peace Prize in 1993 jointly with former President FW de Klerk for ending apartheid and bringing democracy to South Africa.